Lim y->0: Solving (sin 3y * cot 5y) / (y * cot 4y)

[Oneiromancy]

lim y->0 (sin 3y * cot 5y)/(y * cot 4y)

Tricky problem to me. I understand what to do if the problem was something like sin 5x / 4x.

 

[sutupidmath]

Well first rewrite cot in terms of sin and cosine, and look to come up with something sinx/x when x-->0 to some parts of it at least.

 

[rocomath]

\lim_{y\rightarrow 0}\frac{\sin{3y}\cot{5y}}{y\cot{4y}}

 

[Oneiromancy]

\lim_{y\rightarrow 0}\frac{\sin{3y}\cot{5y}}{y\cot{4y}}

Correct. Sorry I'm not good at latex.

 

[rocomath]

\lim_{y\rightarrow 0}\frac{\sin{3y}}{y}\cdot\frac{\sin{4y}}{\cos{4y}}\cdot\frac{\cos{5y}}{\sin{5y}}

How can you manipulate your limit? The left term is very easy.

 

[Oneiromancy]

I know what to do now.

 

[HallsofIvy]

\lim_{y\rightarrow 0}\frac{\sin{3x}}{y}\cdot\frac{\sin{4y}}{\cos{4y}}\cdot\frac{\cos{5y}}{\sin{5y}}

How can you manipulate your limit? The left term is very easy.

It would be easier if it were sin(3y)/y rather than sin(3x)/y !

 

[rocomath]

It would be easier if it were sin(3y)/y rather than sin(3x)/y !

It was a typo!